Wavelets in Applied and Pure Mathematics\
Postgraduate Course in Applied Analysis
Wavelets in Applied and Pure Mathematics
Postgraduate Course in Applied Analysis
University of Leeds,
School of Mathematics
Web page: http://maths.leeds.ac.uk/~kisilv/courses/wavelets.html
Description: The course gives an overview of wavelets (or
coherent states) construction and its realisations in applied
and pure mathematics. After a short introduction to wavelets based on
the representation theory of groups we will consider:
 Spaces of analytic functions with reproducing kernels: the
Hardy and the Bergman spaces, etc.;
 The FockSegalBargmann space and BerezinToeplitz quantisation;
 Functional calculus of selfadjoint operators;
 Elements of signal processing.
The variety of applications is essentially grouped just around
three groups: the Heisenberg group, SL_{2}^{}(R^{}_{}),
and ax+b group.
This course is suitable for postgraduate
students in both applied and pure mathematics.
For online reading lecture notes are available in
PDF (recommended!) or
HTML formats.
See Technical notes on viewing
online materials. To print lecture notes use
PostScript.
Contents:
 What
Are Wavelets and What Are They Good for?

Groups and
Homogeneous Spaces.
 Representation Theory.
 Wavelets on Groups
and Square Integrable Representations.
 Wavelets on
Homogeneous Spaces: the SegalBargmann Space.
 Wavelets in
Banach Spaces and Functional Calculus
Prerequisites: Basic real and complex analysis,
rudimentary algebra.
References
 [1]

Syed Twareque Ali, JeanPierre Antoine, and JeanPierre Gazeau.
Coherent states, wavelets and their generalizations.
Graduate Texts in Contemporary Physics. SpringerVerlag, New York,
2000.
 [2]

Michael E. Taylor.
Noncommutative Harmonic Analysis, volume 22 of Math. Surv.
and Monographs.
American Mathematical Society, Providence, R.I., 1986.
Tecnical Notes:
 If you experienced a problem reading the course HTML pages then
an easy solution could be found in
Help on Browser Problems or (even better) use the PDF files
(see bellow).
 PDF version is provided online and preferable in many
respects.
Acrobat Reader for your computer platform could be obtained free of
charge.
 It is optimal to use AcroRead plugin for your Web
browser. If you use AcroRead as a standalone application,
then for hyperlinks between different PDF files you need to download
all PDF files to the same directory on your computer.
 It is easier to read PDF links if you set the following option in
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File  Preferences  General  Default Page Layout: Continuous
 These pages are created using
free software from L^{A}T_{E}X
source, there are also few
advises on Web publishing.
 Send comments and remarks by email
kisilv@maths.leeds.ac.uk.
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On 22 May 2003, 14:49.